There have been many times where either Tony was no longer acting as Iron Man, no longer building suits, and trying not to be the hero. Before Rhodes was War Machine and became a separate hero, he was piloting the Iron Man armor. Also keep in mind that for a long time, the identity of Iron Man was a secret. The shrapnel was removed from Tony's chest at some point before the Extremis armor was developed, I don't recall exactly when.
In the comic, Extremis was the name of essentially a super soldier serum that granted the recipient crazy, superhuman powers. During the comic arc, Tony modifies Extremis to suit his own needs and builds an armor around it. If you have Netflix, you can watch the
motion comic of the Extremis arc. It's really well made. Before we went to go see the movie, me and a friend of mine (who had never seen it before) watched this and after the movie, he said watching this helped understand what Extremis was and how it worked, because the movie kind of glosses over that.
Anyway, the Mk 42 was vaguely based off of the Extremis armor (the comic Mk 30) because he is able to assemble it on him remotely. The Extremis enhanciles in the movie are similar to the enhanciles in the comic, though a little more simplified.